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Title:ÌýQAOA Versus Classical

Abstract:Ìý

There has been a back and forthÌýabout whether theÌýQAOA algorithm of Farhi, Goldstone and Gutmann can in some sense be duplicatedÌýclassically.

Title:ÌýReverse plane partitions via quiver representations

Abstract:

Let $\lambda$ be a partition. The reverse plane partitions of shape $\lambda$ are a kind of filling of the Ferrers diagram of $\lambda$ by non-negative integers. Richard Stanley found the generating function which enumerates them according to the sum of the entries.

Title:ÌýGraphs in algebra and algebra in graphs

Abstract:

How do algebraic properties of a graph relate to its graph theoretic properties? What are algebraic properties of graphs? What does the spectrum of a graph tell us about its structure? What is a Cayley graph?

Title:ÌýKemeny's Constant for Markov Chains

Abstract:

Markov chains are a much-studied class of stochastic processes, and it is well-known that if the transition matrix A associated with a Markov chain possesses a certain property (called primitivity), then the long-term behaviour of the Markov chain is described by a particular eigenvector of A, known as the stationary distribution vector.

Title:ÌýLewis Carroll and the Red Hot Potato

Abstract:

The Lewis Carroll identity expresses the determinant of a matrix in terms of subdeterminants obtained by deleting one row and column or a pair of rows and columns.

Title:ÌýNew and Simple Algorithms for Stable Flow Problems

Abstract:

In the previous reading group talk we defined stable flows and saw that they always exist by a reduction to the stable allocation problem.

Title:ÌýNon-Commutative Algebras and Graphs

Abstract:

I will discuss some of the non-commutative algebras that arise naturally in graph theory.

Title:ÌýBijections among symmetric tableaux via folding and mixed insertion

Abstract:

A standard Young tableau with entries $-M < \cdots -1 < 1 < \cdots < M$ can be "folded"Ìýby performing certainÌýconversions and rectifications in sequence.

Title:ÌýCounting subdivergence-free gluing of trees

Abstract:

If we take two rooted trees with the same number of leaves and form a graph by gluing the leaves of one tree to the other, then we say the graph is subdivergence-free if no 2-edge cut have been generated.

Title:ÌýThe combinatorics of nearest and furthest values

Abstract:

A classical problem asks us to find, for each element $A[i]$ of an array of integers, the position of the nearest smallest element.